Question

Which is the equation of a line that has a slope of Negative two-thirds and passes through point

(–3, –1)?

Answer 1

D) y = -2/3x - 3

Explanation:

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Answer 2

The equation of a line is
`y=(-2)/(3) x-(5)/(3)`.

Solution:

Given slope, m =
`-(2)/(3)` and passes through the point (–3, –1).

Equation of a line passes through one point and slope formula:

`y-y_1=m(x-x_1)`

Here,
`x_1=-3,y_1=-1` and
`m=-(2)/(3)`

Substitute these in the given formula, we get

⇒
`y-(-1)=(-2)/(3) (x-(-1))`

⇒
`y+1=(-2)/(3) (x+1)`

Cross multiply the fraction.

⇒
`3(y+1)=-2 (x+1)`

⇒
`3y+3=-2x-2`

Subtract 3 on both sides of the equation.

⇒
`3y=-2x-2-3`

⇒
`3y=-2x-5`

Divide by 3 on both sides of the equation.

⇒
`y=(-2)/(3) x-(5)/(3)`

Hence, the equation of a line is
`y=(-2)/(3) x-(5)/(3)`.